4. Show that the sequence {fn}, where nx fn(x)=- xER 1+n°x' is point-wise convergent but is not uniformly convergent in any interval containing zero.
4. Show that the sequence {fn}, where nx fn(x)=- xER 1+n°x' is point-wise convergent but is not uniformly convergent in any interval containing zero.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![4. Show that the sequence {fn}, where
nx
fn(x)=
xER
1+n°x*
is point-wise convergent but is not uniformly convergent in any interval
containing zero.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc51d93eb-f155-4f2b-a13b-dbfb8451cd61%2Ff51c7199-b2fc-4588-8db0-c094a5aadad1%2F4due2jk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:4. Show that the sequence {fn}, where
nx
fn(x)=
xER
1+n°x*
is point-wise convergent but is not uniformly convergent in any interval
containing zero.
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